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Riemannian Geometry of Contact and Symplectic Manifolds
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TLDR
In this article, the authors describe a complex geometry model of Symplectic Manifolds with principal S1-bundles and Tangent Sphere Bundles, as well as a negative Xi-sectional Curvature.Abstract:
Preface * 1. Symplectic Manifolds * 2. Principal S1-bundles * 3. Contact Manifolds * 4. Associated Metrics * 5. Integral Submanifolds and Contact Transformations * 6. Sasakian and Cosymplectic Manifolds * 7. Curvature of Contact Metric Manifolds * 8. Submanifolds of Kahler and Sasakian Manifolds * 9. Tangent Bundles and Tangent Sphere Bundles * 10. Curvature Functionals and Spaces of Associated Metrics * 11. Negative Xi-sectional Curvature * 12. Complex Contact Manifolds * 13. Additional Topics in Complex Geometry * 14. 3-Sasakian Manifolds * Bibliography * Subject Index * Author Indexread more
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Contact 3-manifolds and $*$-Ricci soliton
TL;DR: In this article, it was shown that the Ricci soliton of a 3-dimensional Kenmotsu manifold is locally isometric to the hyperbolic 3-space and the potential vector field coincides with the Reeb vector field.
Symmetry properties of sasakian space forms
TL;DR: In this paper, the authors investigated the pseudo-symmetry of Sasakian space forms for dimension n 6 and showed that there exist pseudo-sakian manifolds which are not semantically symmetric.
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Almost complex structures and calibrated integral cycles in contact 5-manifolds
TL;DR: In this article, it was shown that integral cycles whose approximate tangent planes have the property of being J-invariant are in fact smooth Legendrian curves except possibly at isolated points and investigated how such structures J are related to calibrations.
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Anti-invariant Riemannian Submersions from Kenmotsu Manifolds onto Riemannian manifolds
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Geometry of Spin and Spin^c structures in the M-theory partition function
TL;DR: In this paper, the effects of having multiple spin structures on the partition function of the spacetime fields in M-theory were studied and a potential anomaly appeared in the eta-invariants upon variation of the spin structure.